Particle trajectories in extreme Stokes waves over infinite depth

The pressure distribution in extreme Stokes waves

“…Extending the methods developed in [6] and [10], we demonstrate the aforementioned qualitative behaviour of the pressure in an extreme Stokes wave in fluid body of finite depth; see [11,12,13] for recent results concerning the pressure in deepwater Stokes waves. Pressure measurements within a water body are of significant importance both experimentally and theoretically.…”

“…Moreover, the same technique was employed in the work [9] to prove the convexity of the surface profile of Stokes waves of greatest height. In the recent works [6] and [10], the uniform limiting process was effectively used to show that particles travelling on the streamlines of extremes Stokes waves, in finite and infinite depth, do not form closed trajectories.…”

The dynamic pressure in deep-water extreme Stokes waves

“…This excision method has been successfully utilised to analyse the hydrodynamic pressure in extreme Stokes waves as well as the particle trajectories along streamlines of the flow, in both the deep-water and shallow-water context, cf. [9,33,35,34].…”

The Pressure in a Deep-Water Stokes Wave of Greatest Height

“…The presence of a stagnation point on the free surface presents a number of mathematical difficulties when we try to impose maximum principles on the velocity field (u, v). However a recently developed approach [8,24] has allowed us to circumvent these difficulties by applying maximum principles in an excised domain. We then analyse the dynamical variables u and v and P in a domain with the offending stagnation point removed, and obtain corresponding results for extreme Stokes waves by way of a uniform limiting process.…”